Set Packing and Set Partitioning Problems belong to the class of 0-1 integer programming problems that are NP-complete. Packing problems are a class of optimization problems in mathematics which involves attempting to pack objects, as densely as possible but optimally, many applications arise having the packing and partitioning structure.
Delivery and routing problems, scheduling problems and location problems, switching theory, wireless network design, VLSI circuits and line balancing often take on a set packing structure, if one wishes to satisfy as much demand as possible without creating conflict and, if every customer must be served by exactly one server, the problem takes on a set partitioning format. The Set Packing Problem has a dual covering problem, which asks how many of the same objects are
required to completely cover every region of the container, where the objects are allowed to overlap. In this paper a linearization technique is developed to solve packing problems with non-linear objective function, in particular the quadratic objective function. This is an extension of the work done by Saxena and Arora . The algorithms redeveloped
in this paper are supported by numerical examples.